As long as you noticed some redness around the follicles, you should have had a sufficient treatment. The hair that is treated takes time to fall out and should not grow back. The hairs you see now might be the growth of a new cycle of hair that will be treated at your next session. 6 to 8 treatments of an area for laser hair reduction is standard.
With any laser hair removal treatment, one week post-procedure is too early to judge. Laser hair removal works like this: after the hair is treated with the laser, it will appear to grow as normal until shedding approximately 1-3 weeks following treatment. After shedding, depending on the individual, it can take anywhere from 1-2 months before any regrowth is noted. Of course, not all hairs will follow this cycle at the same time as only hairs in growth phase are affected by the laser and at the time of any given treatment, not all hairs will be in that phase. You can expect around a 20% reduction in hair per treatment, hence the need for multiple treatments. Now whether or not your doctor paid sufficient attention or used the best laser, I cannot say, however I can say that the process of laser hair removal and what to expect should've been explained to you, if it was not. If you do feel comfortable pursuing treatment with this doctor, I would give it a bit more time before making any judgements.